High-frequency (i.e., >15 MHz) ultrasound (HFU) provides fine-resolution images on the order of 100 um because of its short wavelengths (i.e., <100 um) and small focal-zone beam diameters. HFU is able to acquire 3D data in a manner of minutes with the potential to provide real time dynamic information. Because of its rapid data acquisition and commercial availability, HFU has become a promising tool. Both Quantitative ultrasound and HFU are used to study morphology and/or organ function. The data acquired is rich in information and an automated method for studying features and properties of such data is beneficial. Such studies may require the segmentation of the data to properly analyze and characterize the different structures within the images being studied, for example structures within a developing embryo or normal and abnormal tissues of the human lymph node.
To obtain satisfactory segmentation, accurate intensity distributions are required. Some clustering algorithms, such as K-means or expectation maximization (EM), may be able to categorize the intensity value of all voxels into distributions to represent target objects. However, these approaches often yield unsatisfactory segmentation results, where the intensity fluctuates with depth significantly because of acoustic attenuation and focusing effects. A possible solution is to divide the image into several bands at specified depths, and apply clustering algorithms in each band. In addition, attenuation effects may become so extreme that certain boundaries become invisible. To mitigate similar attenuation and missing-boundary problems in prostate segmentation, “Prostate Segmentation in Echographic Images: A Variational Approach Using Deformable Super-Ellipse and Rayleigh Distribution,” by Saroul et al. proposed a level-set based method. In the proposed approach, a super-ellipse model is used to preserve the shape, and Rayleigh distributions are used to model the intensity distributions in different subsections. The intensity distributions are updated with deformation to overcome the effect of attenuation, but this method requires proper initialization.
Another method, active shape model (ASM), segments objects with missing boundaries using the shape models from manually segmented data. However, ASM requires a dense set of feature points to appropriately model the details of complex shapes. A hybrid method has been developed that combines ASM and shape-constrained region growing to reduce the number of feature points. However, to capture the shape variations between different datasets, a large number of manually segmented datasets are necessary to generate a sufficient number of eigen-shapes. In practice, such manual segmentation may not be feasible.
Instead of using specific shape models, incorporation of structural constraints into image segmentation algorithms has gained attention in recent years. Some methods represent the structural prior between objects by a tree structure, where the leaves represent the objects and branch nodes represent groups, and exploit the tree structure when determining the segmentation sequence or solving a hierarchical cost. There have been several prior studies on using graph cuts to segment multiple objects with structural constraints including studies by Ishikawa, Delong and Boykov.
“Exact Optimization for Markov Random Fields with Convex Priors,” by H. Ishikawa proposed to represent multiple objects by separated layers of a graph stacked together as a “layer cake” with linearly ordered labels for successive layers. If a regularization term is convex in terms of a linearly ordered label set, this multi-object segmentation problem can be solved as a binary graph cut problem, but fails to take advantage of specific relationships among objects. In Ishikawa's model, the foreground in an upper layer is restricted to be a subset of the foreground in the layer below by using directed interlayer edges with an infinite cost. Although how to incorporate structural constraints with this layer-cake structure was not addressed, Ishikawa's model has been widely used in segmenting objects with a recurring “containment” relationship. The regularization cost of Ishikawa's model is not discontinuity-preserving, which means that the cost between two pixels increases with the difference of their labels. “Globally Optimal Segmentation of Multi-Region Objects,” by A. Delong and Y. Boykov proposed to make use of the known generic relationships between multiple objects such as “containment,” “attraction,” and “exclusion.” Delong and Boykov's model also uses a set of layers to represent all objects as in Ishikawa's model, but all these layers are unordered and connected by inter-layer edges according to structural relationships. The known structural constraints are enforced by assigning proper costs along these directed inter-layer edges. Delong and Boykov's model can enforce a containment relationship, as in Ishikawa's model, and enforce an exclusion relationship, but there exists some restriction for the combination of relationships. Other proposed models include those by Li et al. and Nosrati. “Optimal Surface Segmentation in Volumetric Images—A Graph Theoretic Approach,” by K. Li et al. proposed a graphical-based method using detachment constraints but is only applicable to cylindrical or spherical objects. “Local Optimization Based Segmentation of Spatially-recurring, Multi-Region Objects with Part Configuration Constraints,” by Nosrati et al proposed a level-set-based method to segment spatially recurring objects with detachment relationships.
However, in situations where there are missing boundaries, detachment and attraction constraints cannot help to define the missing boundary, and therefore previously discussed graph-cut-based or level-set-based methods cannot obtain correct segmentation results without using sufficient initial seeds or adding extra parameters such as different weights for region regularizations.